WMA11 Jan 2021

2. WMA11/01 Edexcel IAL P1 January 2021 IAL Q2 (Simultaneous Equations)

A tree was planted.​​ 

Exactly 3 years after it was planted, the height of the tree was 2m.​​ 

Exactly 5 years after​​ it was planted, the height of the tree was 2.4m.​​ 

Given that the height, H metres, of the tree, t years after it was planted, can be modelled by the equation​​ 

H3 = pt2 + q 

where p and q are constants,​​ 

• find, to 3 significant figures where necessary, the value of p and the value of q.​​ 

(4)

Exactly T years after the tree was planted, its height was 5m.​​ 

• Find the value of T according to the model, giving your answer to one decimal place.​​ 

(2)

SOLUTION

a-​​ 

Putting​​ t=3, & H=2

23=p32+q

8=pq+q     -1

Putting​​ t=5 ,  H=2.4

2.43=p52+q  

13.82=25p+q      -2

Now, on subtracting equation 1 by 2, we get

5.824=16p

p=5.82416

p=0.364

Substituting the value of of p in equation 1 or 2. Here we are subtituting in equation 1.

8=pq+q

q=8-9p

q=8-90.364

q=4.724

Hence, the values of p and q are​​ 

p=0.364& q=4.724

b-​​ 

To find the value of T when the height of tree is 5m, substitute the value 5m in the modelled eqaution, provided in the​​ question.​​ 

H3 =0.364t2+4.724

53=0.364T2+ 4.724

T=125-4.7240.364

T=18.17769….

T=18.2 years